On the existence of extremal type II ℤ2k-codes

Masaaki Harada; Tsuyoshi Miezaki

doi:10.1090/S0025-5718-2013-02750-0

On the existence of extremal type II ℤ_2k-codes

Masaaki Harada^*, Tsuyoshi Miezaki

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

For lengths 8, 16, and 24, it is known that there is an extremal Type II ℤ_2k-code for every positive integer k. In this paper, we show that there is an extremal Type II ℤ_2k-code of lengths 32, 40, 48, 56, and 64 for every positive integer k. For length 72, it is also shown that there is an extremal Type II ℤ4k-code for every positive integer k with k ≥ 2.

Original language	English
Pages (from-to)	1427-1446
Number of pages	20
Journal	Mathematics of Computation
Volume	83
Issue number	287
DOIs	https://doi.org/10.1090/S0025-5718-2013-02750-0
Publication status	Published - 2014 May
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

Access to Document

10.1090/S0025-5718-2013-02750-0

Cite this

@article{7b9918c3946e4656bdb520a7e77e9664,

title = "On the existence of extremal type II ℤ2k-codes",

abstract = "For lengths 8, 16, and 24, it is known that there is an extremal Type II ℤ2k-code for every positive integer k. In this paper, we show that there is an extremal Type II ℤ2k-code of lengths 32, 40, 48, 56, and 64 for every positive integer k. For length 72, it is also shown that there is an extremal Type II ℤ4k-code for every positive integer k with k ≥ 2.",

author = "Masaaki Harada and Tsuyoshi Miezaki",

year = "2014",

month = may,

doi = "10.1090/S0025-5718-2013-02750-0",

language = "English",

volume = "83",

pages = "1427--1446",

journal = "Mathematics of Computation",

issn = "0025-5718",

publisher = "American Mathematical Society",

number = "287",

}

TY - JOUR

T1 - On the existence of extremal type II ℤ2k-codes

AU - Harada, Masaaki

AU - Miezaki, Tsuyoshi

PY - 2014/5

Y1 - 2014/5

N2 - For lengths 8, 16, and 24, it is known that there is an extremal Type II ℤ2k-code for every positive integer k. In this paper, we show that there is an extremal Type II ℤ2k-code of lengths 32, 40, 48, 56, and 64 for every positive integer k. For length 72, it is also shown that there is an extremal Type II ℤ4k-code for every positive integer k with k ≥ 2.

AB - For lengths 8, 16, and 24, it is known that there is an extremal Type II ℤ2k-code for every positive integer k. In this paper, we show that there is an extremal Type II ℤ2k-code of lengths 32, 40, 48, 56, and 64 for every positive integer k. For length 72, it is also shown that there is an extremal Type II ℤ4k-code for every positive integer k with k ≥ 2.

UR - http://www.scopus.com/inward/record.url?scp=84894860898&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894860898&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-2013-02750-0

DO - 10.1090/S0025-5718-2013-02750-0

M3 - Article

AN - SCOPUS:84894860898

SN - 0025-5718

VL - 83

SP - 1427

EP - 1446

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 287

ER -

On the existence of extremal type II ℤ_2k-codes

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this